// Copyright (c) 2007, 2008 libmv authors.
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to
// deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
// sell copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
// IN THE SOFTWARE.

// Copyright (c) 2012, 2013 Pierre MOULON.

// This Source Code Form is subject to the terms of the Mozilla Public
// License, v. 2.0. If a copy of the MPL was not distributed with this
// file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef OPENMVG_NUMERIC_POLY_H_
#define OPENMVG_NUMERIC_POLY_H_

#include <cmath>
#include <stdio.h>

namespace openMVG {

// Solve the cubic polynomial
//
//   x^3 + a*x^2 + b*x + c = 0
//
// The number of roots (from zero to three) is returned. If the number of roots
// is less than three, then higher numbered x's are not changed. For example,
// if there are 2 roots, only x0 and x1 are set.
//
// The GSL cubic solver was used as a reference for this routine.
template <typename Real> int SolveCubicPolynomial(Real a, Real b, Real c, Real *x0, Real *x1, Real *x2) {
    Real q = a * a - 3 * b;
    Real r = 2 * a * a * a - 9 * a * b + 27 * c;

    Real Q = q / 9;
    Real R = r / 54;

    Real Q3 = Q * Q * Q;
    Real R2 = R * R;

    Real CR2 = 729 * r * r;
    Real CQ3 = 2916 * q * q * q;

    if (R == 0 && Q == 0) {
        // Tripple root in one place.
        *x0 = *x1 = *x2 = -a / 3;
        return 3;

    } else if (CR2 == CQ3) {
        // This test is actually R2 == Q3, written in a form suitable for exact
        // computation with integers.
        //
        // Due to finite precision some double roots may be missed, and
        // considered
        // to be a pair of complex roots z = x +/- epsilon i close to the real
        // axis.
        Real sqrtQ = sqrt(Q);
        if (R > 0) {
            *x0 = -2 * sqrtQ - a / 3;
            *x1 = sqrtQ - a / 3;
            *x2 = sqrtQ - a / 3;
        } else {
            *x0 = -sqrtQ - a / 3;
            *x1 = -sqrtQ - a / 3;
            *x2 = 2 * sqrtQ - a / 3;
        }
        return 3;

    } else if (CR2 < CQ3) {
        // This case is equivalent to R2 < Q3.
        Real sqrtQ = sqrt(Q);
        Real sqrtQ3 = sqrtQ * sqrtQ * sqrtQ;
        Real theta = acos(R / sqrtQ3);
        Real norm = -2 * sqrtQ;
        *x0 = norm * cos(theta / 3) - a / 3;
        *x1 = norm * cos((theta + 2.0 * M_PI) / 3) - a / 3;
        *x2 = norm * cos((theta - 2.0 * M_PI) / 3) - a / 3;

        // Put the roots in ascending order.
        if (*x0 > *x1) {
            std::swap(*x0, *x1);
        }
        if (*x1 > *x2) {
            std::swap(*x1, *x2);
            if (*x0 > *x1) {
                std::swap(*x0, *x1);
            }
        }
        return 3;
    }
    Real sgnR = (R >= 0 ? 1 : -1);
    Real A = -sgnR * pow(fabs(R) + sqrt(R2 - Q3), 1.0 / 3.0);
    Real B = Q / A;
    *x0 = A + B - a / 3;
    return 1;
}

// The coefficients are in ascending powers, i.e. coeffs[N]*x^N.
template <typename Real> int SolveCubicPolynomial(const Real *coeffs, Real *solutions) {
    if (coeffs[0] == 0.0) {
        // TODO(keir): This is a quadratic not a cubic. Implement a quadratic
        // solver!
        return 0;
    }
    Real a = coeffs[2] / coeffs[3];
    Real b = coeffs[1] / coeffs[3];
    Real c = coeffs[0] / coeffs[3];
    return SolveCubicPolynomial(a, b, c, solutions + 0, solutions + 1, solutions + 2);
}
} // namespace openMVG
#endif // OPENMVG_NUMERIC_POLY_H_
